Lecture 18: The Modeling
Environment
CE 498/698 and ERS 485
Principles of Water Quality
Modeling
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
1
The modeling environment
• Models are an idealized formulation that
represents the response of a physical
system to external stimuli (p. 10)
• Models are tools that are part of an
overall management process
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
2
Data
collection
Management
(or scientific)
objectives,
options,
constraints
CE 498/698 and ERS 685
(Spring 2004)
Make
management
decisions
Model
development
and
application
Lecture 18
3
Rules of modeling
• RULE 1: We cannot model reality
– We have to make assumptions
• DOCUMENT!!!!
• RULE 2: Real world has less precision
than modeling
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
4
Precision vs. accuracy
• Precision
– Number of decimal places
– Spread of repeated computations
• Accuracy
– Error between computed or measured
value and true value
error of
= field error + model error
estimate
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
5
The problem with precise
models…
we get more precision from
model than is real
Model says…
Difference = 10.056 deg C
Location B
Location A
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
6
Figure 18.1 (Chapra 1997)
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
7
Modeling in management
process
• Problem specification
• Do we need to model?
• Model selection
– Who will the users be?
– What kind of data is available?
– General model or specific?
– Use existing model or develop a new one?
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
8
Modeling in management
process
• Model development
– Develop/modify code
– Input data
– Determine numerical approach
• model resolution
– Timestep
– Spatial size
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
9
Figure 18.9 (Chapra 1997)
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
10
Modeling in management
process
• Model development
– Develop/modify code
– Input data
– Determine numerical approach
• model resolution
– Timestep
– Spatial size
– Matter
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
11
Modeling in management
process
• Preliminary application and calibration
Figure 18.3 (Chapra 1997)
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
12
Modeling in management
process
• Preliminary application and calibration
– Adjust parameters
– Adjust input data (where appropriate)
– Compare model predictions with measured
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
13
Calibration measures
• Chapra: minimize sum of squares of
n
2
residuals
Minimize S r   c p ,i  cm,i 
i 1
where cp,i = model prediction for i
cm,i = measured value for i
smallest sum is best!
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
14
Calibration measures
• Chapra: minimize sum of squares of
n
2
residuals
Minimize S r   c p ,i  cm,i 
i 1
• R-squared: how much of the variability
in the observed data is explained by the
n
2
predicted data
 c p ,i  cm ,i 
r 2  1
0 ≤ r2 ≤ 1
CE 498/698 and ERS 685
(Spring 2004)
i 1
  c 
n
 
cm2 ,i    i1 
 i 1 
n
Lecture 18
n
2
2
m ,i
15
Calibration measures
• Average absolute error
n
 absc p ,i  cm,i 
Minimize ABSE  i1
n
• Root mean squared error
 c
n
Minimize RMSE 
i 1
p ,i  cm ,i 
2
n
Calibration is a KEY process!
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
16
Modeling in management
process
• Model confirmation (validation)
– Use an independent data set for measured
values
– Use same parameters/coefficients, same
methods of estimating data
• Does model still work????
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
17
Modeling in management
process
• Management application
• Verification
• Sensitivity analysis
CE 498/698 and ERS 685
(Spring 2004)
Lecture 18
18